Theorems · Theorem · harmonic analysis
hasSum_fourier_series_L2
- #76 of the 100 theorems: Fourier Series
∀ {T : ℝ} [hT : Fact (0 < T)] (f : ↥(MeasureTheory.Lp ℂ 2 AddCircle.haarAddCircle)),
HasSum (fun i => fourierCoeff (↑↑f) i • fourierLp 2 i) fThe Fourier series of an L2 function f sums to f, in the L² space of AddCircle T.
- Defined in
- Mathlib.Analysis.Fourier.AddCircle
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 272 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fact
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- ENNRealstatement · cited by 9,879
- Complexstatement and proof · cited by 5,565
- AddSubgroupstatement · cited by 3,232
- Factstatement and proof · cited by 2,726
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- MeasureTheory.AEEqFunstatement and proof · cited by 856
- MeasureTheory.Lpstatement and proof · cited by 715
- HasSumstatement and proof · cited by 518
- AddSubgroup.zmultiplesstatement · cited by 493
- MeasureTheory.AEEqFun.caststatement · cited by 380
Cited by1
Results whose statement or proof uses this declaration.
- hasSum_fourier_series_of_summableproof · cited by 1